Equalization of the Element Radiation Paterns for Root Based Direction Finding Algorithms

Root based direction finding (DF) algorithms presume equal element radiation patterns in the terminated array environment, a requirement that can generally not be satisfied due to mutual coupling. In this paper a technique is investigated for improving the direction of arrival (DOA) estimation accuracy of root based DF algorithms through equalization of element patterns of centrally located “active” elements in a linear array by appending passively terminated “dummy” elements at both ends of the array. An iterative nonlinear optimization algorithm is employed to determine the optimum terminating impedances. A numerical example of a 10 -element dipole array shows a significant reduction in the DOA estimation error. INTRODUCTION Root based super-resolution DF algorithms such as Root-MUSIC [1], [2], and Modified Root Pisarenko (MRP) [1], offer computational efficiency but assume equal element radiation patterns in the terminated array environment. Because of mutual coupling this requirement is generally not met so that root-based DF algorithms necessarily suffer a loss in accuracy unless some form of compensation is employed [1][3]. One way to attain approximate equality among the radiation patterns is to employ a decoupling transform [1]. Another approach is to exploit symmetry. For a linear array of uniformly spaced elements the concept of an infinite antenna array affords the appropriate paradigm. Thus, by adding a few passively terminated elements at both ends of a finite length array, some degree of approximation to the infinite array environment can be achieved, resulting in improvement in DOA estimation accuracy [4]. While the simplest approach is to select for the passive terminations the same impedances as for the active (receiving) elements [4] (e.g., 50 Ω) we have also investigated the additional possibility of determining the passive terminating impedances that minimize the inequality among the element patterns of the active array elements and using these optimum impedances as passive terminations. Our test bed for the numerical investigation is a 10element dipole array with 4 active centrally located (receiving) elements and 3 passively terminated elements on either end. The DOA calculations are carried out using the MRP algorithm [1] for two incident signals as a function of relative angular separation. The results show that optimizing the terminations of the passive elements leads to significant improvements in DOA estimation accuracy, especially as the angular separation between the incident signals decreases. OPTIMIZATION PROCEDURE Fig.1 shows a schematic representation of a linear array comprising 10 physically identical elements where the 4 central active elements are assumed connected to four separate receivers each with 50 Ω input impedance, while the impedances for the 6 passive elements remain to be determined. Fig 1. 10-elements linear array with 6 passive and 4 active elements terminated with . 50Ω